Have left them as long as 10 or so days. Put a brick etc under the opposite end of the drain and add ice as needed. Water stays drained that way.
I usually only ice it long enough to firm up the meat. Shot two deer this weekend my wifes buck was on ice for about 2 hours before we fully processed him and I shot my doe late so we iced her over night and finished processing in morning. You wont gain anything I have noticed by leaving it on ice extended periods of time. We ate steaks out of the buck Monday and Tuesday night and they were excellent.
It's hell eatin em live